When a thin convex lens is placed in contact with a concave mirror of the same focal length,the resultant focal length of the system is ......

The diagram shows a silvered equiconvex lens. An object of length $1\,cm$ is placed at a distance of $30\,cm$ in front of the lens. What will be the final image properties? The refractive index of the lens is $\mu$ and the refractive index of the medium in which the lens has been placed is $2\mu$. Both surfaces have a radius of curvature $R$.

An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be

The flat face of a plano-convex lens of focal length $10 \,cm$ is silvered. $A$ point source placed $30 \,cm$ in front of the curved surface will produce a

The two surfaces of a biconvex lens have the same radii of curvature. This lens is made of glass of refractive index $1.5$ and has a focal length $10 \ cm$ in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index $= 4/3$), its focal length (in $cm$) is:

$A$ double convex lens of focal length $F$ is cut into two equal parts along the vertical axis. The focal length of each part will be